Protein secondary and tertiary structures are essential determinants of molecular function. Thus, the problem of developing correct predictions of secondary and tertiary structures of proteins of known amino acid sequences is central to modern protein physical chemistry. The Monte Carlo method is one of the most popular techniques used to predict protein secondary and tertiary structure. In this proposal, two new Monte Carlo simulation algorithms specially tailored for the prediction of peptide and protein secondary and tertiary structures are proposed. These algorithms will use an extended formulation of Markov chain Monte Carlo sampling method. This formulation shows that a correct sample can be obtained when different types of random moves are performed according to some pattern in a Monte Carlo algorithm. The first algorithm is Entropy Sampling Monte Carlo (ESMC) and the second is standard Monte Carlo (SMC). Two types of random moves will be included in both algorithms. The first type of move is guided by local intramolecular interactions; therefore, it is computationally cheap and efficient. The second type of move mimics energy minimization in a probabilistic way. These moves can help to find low-energy conformations in simulations. ESMC is better in overcoming energy barriers, while SMC is more efficient for simulations of short peptides.